General exact solvability conditions for the initial value problems for linear fractional functional differential equations

Natalia Dilna

Archivum Mathematicum (2023)

  • Volume: 059, Issue: 1, page 11-19
  • ISSN: 0044-8753

Abstract

top
Conditions on the unique solvability of linear fractional functional differential equations are established. A pantograph-type model from electrodynamics is studied.

How to cite

top

Dilna, Natalia. "General exact solvability conditions for the initial value problems for linear fractional functional differential equations." Archivum Mathematicum 059.1 (2023): 11-19. <http://eudml.org/doc/298969>.

@article{Dilna2023,
abstract = {Conditions on the unique solvability of linear fractional functional differential equations are established. A pantograph-type model from electrodynamics is studied.},
author = {Dilna, Natalia},
journal = {Archivum Mathematicum},
keywords = {fractional order functional differential equations; Caputo derivative; normal and reproducing cone; unique solvability},
language = {eng},
number = {1},
pages = {11-19},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {General exact solvability conditions for the initial value problems for linear fractional functional differential equations},
url = {http://eudml.org/doc/298969},
volume = {059},
year = {2023},
}

TY - JOUR
AU - Dilna, Natalia
TI - General exact solvability conditions for the initial value problems for linear fractional functional differential equations
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 059
IS - 1
SP - 11
EP - 19
AB - Conditions on the unique solvability of linear fractional functional differential equations are established. A pantograph-type model from electrodynamics is studied.
LA - eng
KW - fractional order functional differential equations; Caputo derivative; normal and reproducing cone; unique solvability
UR - http://eudml.org/doc/298969
ER -

References

top
  1. Aphithana, A., Ntouyas, S.K., Tariboon, J., 10.1186/s13661-015-0329-1, Bound. Value Probl. 2015 (68) (2015), 14 pp., https://doi.org/10.1186/s13661-015-0329-1. (2015) MR3338722DOI10.1186/s13661-015-0329-1
  2. Diethelm, K., The Analysis of Fractional Differential Equations. An Application-Oriented Exposition Using Differential Operators of Caputo Type, Springer, 2010. (2010) Zbl1215.34001MR2680847
  3. Dilna, N., Exact solvability conditions for the model with a discrete memory effect, International Conference on Mathematical Analysis and Applications in Science and Engineering, Book of Extended Abstracts, 2022, 405–407 pp. (2022) 
  4. Dilna, N., Fečkan, M., 10.3390/math10101759, Mathematics 10 (10) (2022), 1759, https://doi.org/10.3390/math10101759. (2022) MR4563012DOI10.3390/math10101759
  5. Dilna, N., Gromyak, M., Leshchuk, S., 10.1007/s10958-022-06072-8, J. Math. Sci. 265 (2022), 577–588, https://doi.org/10.1007/s10958-022-06072-8. (2022) MR4518887DOI10.1007/s10958-022-06072-8
  6. Fečkan, M., Marynets, K., 10.1140/epjst/e2018-00017-9, The European Physical Journal Special Topics 226 (2017), 3681–3692, https://doi.org/10.1140/epjst/e2018-00017-9. (2017) DOI10.1140/epjst/e2018-00017-9
  7. Fečkan, M., Wang, J.R., Pospíšil, M., Fractional-Order Equations and Inclusions, 1st. ed., Walter de Gruyter GmbH, Berlin, Boston, 2017. (2017) 
  8. Gautam, G.R., Dabas, J., 10.1007/s13348-016-0189-8, Collect. Math 69 (2018), 25–37. (2018) MR3742978DOI10.1007/s13348-016-0189-8
  9. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and Applications of Fractional Differential Equations, Elsevier B.P., 2006. (2006) Zbl1092.45003MR2218073
  10. Opluštil, Z., 10.1007/s11072-009-0038-8, Nonlinear Oscil. 11 (3) (2008), 365–386. (2008) MR2512754DOI10.1007/s11072-009-0038-8
  11. Patade, J., Bhalekar, S., 10.1515/psr-2016-5103, Phys. Sci. Rev. Inform. 9 (2017), 20165103 https://doi.org/10.1515/psr-2016-5103. (2017) DOI10.1515/psr-2016-5103
  12. Reed, M., Simon, B., Methods of modern mathematical physics, Acad. Press, New York-London, 1972. (1972) 
  13. Rontó, A., Rontó, M., Successive Approximation Techniques in Non-Linear Boundary Value Problems, Handbook of Differential Equations: Ordinary Differential Equations, Elsevier, New York, 2009, pp. 441–592. (2009) MR2440165
  14. Šremr, J., 10.21136/MB.2007.134126, Math. Bohem. 132 (2007), 263–295. (2007) MR2355659DOI10.21136/MB.2007.134126

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.